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<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.preprocessing</span></code>.PolynomialFeatures</a><ul>
<li><a class="reference internal" href="#examples-using-sklearn-preprocessing-polynomialfeatures">Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.preprocessing.PolynomialFeatures</span></code></a></li>
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  <div class="section" id="sklearn-preprocessing-polynomialfeatures">
<h1><a class="reference internal" href="../classes.html#module-sklearn.preprocessing" title="sklearn.preprocessing"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.preprocessing</span></code></a>.PolynomialFeatures<a class="headerlink" href="#sklearn-preprocessing-polynomialfeatures" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="sklearn.preprocessing.PolynomialFeatures">
<em class="property">class </em><code class="sig-prename descclassname">sklearn.preprocessing.</code><code class="sig-name descname">PolynomialFeatures</code><span class="sig-paren">(</span><em class="sig-param">degree=2</em>, <em class="sig-param">interaction_only=False</em>, <em class="sig-param">include_bias=True</em>, <em class="sig-param">order='C'</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/preprocessing/_data.py#L1369"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures" title="Permalink to this definition">¶</a></dt>
<dd><p>Generate polynomial and interaction features.</p>
<p>Generate a new feature matrix consisting of all polynomial combinations
of the features with degree less than or equal to the specified degree.
For example, if an input sample is two dimensional and of the form
[a, b], the degree-2 polynomial features are [1, a, b, a^2, ab, b^2].</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>degree</strong><span class="classifier">integer</span></dt><dd><p>The degree of the polynomial features. Default = 2.</p>
</dd>
<dt><strong>interaction_only</strong><span class="classifier">boolean, default = False</span></dt><dd><p>If true, only interaction features are produced: features that are
products of at most <code class="docutils literal notranslate"><span class="pre">degree</span></code> <em>distinct</em> input features (so not
<code class="docutils literal notranslate"><span class="pre">x[1]</span> <span class="pre">**</span> <span class="pre">2</span></code>, <code class="docutils literal notranslate"><span class="pre">x[0]</span> <span class="pre">*</span> <span class="pre">x[2]</span> <span class="pre">**</span> <span class="pre">3</span></code>, etc.).</p>
</dd>
<dt><strong>include_bias</strong><span class="classifier">boolean</span></dt><dd><p>If True (default), then include a bias column, the feature in which
all polynomial powers are zero (i.e. a column of ones - acts as an
intercept term in a linear model).</p>
</dd>
<dt><strong>order</strong><span class="classifier">str in {‘C’, ‘F’}, default ‘C’</span></dt><dd><p>Order of output array in the dense case. ‘F’ order is faster to
compute, but may slow down subsequent estimators.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 0.21.</span></p>
</div>
</dd>
</dl>
</dd>
<dt class="field-even">Attributes</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>powers_</strong><span class="classifier">array, shape (n_output_features, n_input_features)</span></dt><dd><p>powers_[i, j] is the exponent of the jth input in the ith output.</p>
</dd>
<dt><strong>n_input_features_</strong><span class="classifier">int</span></dt><dd><p>The total number of input features.</p>
</dd>
<dt><strong>n_output_features_</strong><span class="classifier">int</span></dt><dd><p>The total number of polynomial output features. The number of output
features is computed by iterating over all suitably sized combinations
of input features.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>Be aware that the number of features in the output array scales
polynomially in the number of features of the input array, and
exponentially in the degree. High degrees can cause overfitting.</p>
<p>See <a class="reference internal" href="../../auto_examples/linear_model/plot_polynomial_interpolation.html#sphx-glr-auto-examples-linear-model-plot-polynomial-interpolation-py"><span class="std std-ref">examples/linear_model/plot_polynomial_interpolation.py</span></a></p>
<p class="rubric">Examples</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">PolynomialFeatures</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">6</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">X</span>
<span class="go">array([[0, 1],</span>
<span class="go">       [2, 3],</span>
<span class="go">       [4, 5]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">poly</span> <span class="o">=</span> <span class="n">PolynomialFeatures</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">poly</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="go">array([[ 1.,  0.,  1.,  0.,  0.,  1.],</span>
<span class="go">       [ 1.,  2.,  3.,  4.,  6.,  9.],</span>
<span class="go">       [ 1.,  4.,  5., 16., 20., 25.]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">poly</span> <span class="o">=</span> <span class="n">PolynomialFeatures</span><span class="p">(</span><span class="n">interaction_only</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">poly</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="go">array([[ 1.,  0.,  1.,  0.],</span>
<span class="go">       [ 1.,  2.,  3.,  6.],</span>
<span class="go">       [ 1.,  4.,  5., 20.]])</span>
</pre></div>
</div>
<p class="rubric">Methods</p>
<table class="longtable docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.preprocessing.PolynomialFeatures.fit" title="sklearn.preprocessing.PolynomialFeatures.fit"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code></a>(self, X[, y])</p></td>
<td><p>Compute number of output features.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.preprocessing.PolynomialFeatures.fit_transform" title="sklearn.preprocessing.PolynomialFeatures.fit_transform"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit_transform</span></code></a>(self, X[, y])</p></td>
<td><p>Fit to data, then transform it.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.preprocessing.PolynomialFeatures.get_feature_names" title="sklearn.preprocessing.PolynomialFeatures.get_feature_names"><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_feature_names</span></code></a>(self[, input_features])</p></td>
<td><p>Return feature names for output features</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.preprocessing.PolynomialFeatures.get_params" title="sklearn.preprocessing.PolynomialFeatures.get_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_params</span></code></a>(self[, deep])</p></td>
<td><p>Get parameters for this estimator.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.preprocessing.PolynomialFeatures.set_params" title="sklearn.preprocessing.PolynomialFeatures.set_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code></a>(self, \*\*params)</p></td>
<td><p>Set the parameters of this estimator.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.preprocessing.PolynomialFeatures.transform" title="sklearn.preprocessing.PolynomialFeatures.transform"><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code></a>(self, X)</p></td>
<td><p>Transform data to polynomial features</p></td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="sklearn.preprocessing.PolynomialFeatures.__init__">
<code class="sig-name descname">__init__</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">degree=2</em>, <em class="sig-param">interaction_only=False</em>, <em class="sig-param">include_bias=True</em>, <em class="sig-param">order='C'</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/preprocessing/_data.py#L1440"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures.__init__" title="Permalink to this definition">¶</a></dt>
<dd><p>Initialize self.  See help(type(self)) for accurate signature.</p>
</dd></dl>

<dl class="method">
<dt id="sklearn.preprocessing.PolynomialFeatures.fit">
<code class="sig-name descname">fit</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">X</em>, <em class="sig-param">y=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/preprocessing/_data.py#L1494"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures.fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute number of output features.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">array-like, shape (n_samples, n_features)</span></dt><dd><p>The data.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">instance</span></dt><dd></dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.preprocessing.PolynomialFeatures.fit_transform">
<code class="sig-name descname">fit_transform</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">X</em>, <em class="sig-param">y=None</em>, <em class="sig-param">**fit_params</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/base.py#L544"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures.fit_transform" title="Permalink to this definition">¶</a></dt>
<dd><p>Fit to data, then transform it.</p>
<p>Fits transformer to X and y with optional parameters fit_params
and returns a transformed version of X.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">numpy array of shape [n_samples, n_features]</span></dt><dd><p>Training set.</p>
</dd>
<dt><strong>y</strong><span class="classifier">numpy array of shape [n_samples]</span></dt><dd><p>Target values.</p>
</dd>
<dt><strong>**fit_params</strong><span class="classifier">dict</span></dt><dd><p>Additional fit parameters.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>X_new</strong><span class="classifier">numpy array of shape [n_samples, n_features_new]</span></dt><dd><p>Transformed array.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.preprocessing.PolynomialFeatures.get_feature_names">
<code class="sig-name descname">get_feature_names</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">input_features=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/preprocessing/_data.py#L1464"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures.get_feature_names" title="Permalink to this definition">¶</a></dt>
<dd><p>Return feature names for output features</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>input_features</strong><span class="classifier">list of string, length n_features, optional</span></dt><dd><p>String names for input features if available. By default,
“x0”, “x1”, … “xn_features” is used.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>output_feature_names</strong><span class="classifier">list of string, length n_output_features</span></dt><dd></dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.preprocessing.PolynomialFeatures.get_params">
<code class="sig-name descname">get_params</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">deep=True</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/base.py#L173"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures.get_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Get parameters for this estimator.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>deep</strong><span class="classifier">bool, default=True</span></dt><dd><p>If True, will return the parameters for this estimator and
contained subobjects that are estimators.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>params</strong><span class="classifier">mapping of string to any</span></dt><dd><p>Parameter names mapped to their values.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.preprocessing.PolynomialFeatures.set_params">
<code class="sig-name descname">set_params</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">**params</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/base.py#L205"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures.set_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Set the parameters of this estimator.</p>
<p>The method works on simple estimators as well as on nested objects
(such as pipelines). The latter have parameters of the form
<code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s possible to update each
component of a nested object.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>**params</strong><span class="classifier">dict</span></dt><dd><p>Estimator parameters.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">object</span></dt><dd><p>Estimator instance.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.preprocessing.PolynomialFeatures.transform">
<code class="sig-name descname">transform</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">X</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/preprocessing/_data.py#L1516"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures.transform" title="Permalink to this definition">¶</a></dt>
<dd><p>Transform data to polynomial features</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>X</strong><span class="classifier">array-like or CSR/CSC sparse matrix, shape [n_samples, n_features]</span></dt><dd><p>The data to transform, row by row.</p>
<p>Prefer CSR over CSC for sparse input (for speed), but CSC is
required if the degree is 4 or higher. If the degree is less than
4 and the input format is CSC, it will be converted to CSR, have
its polynomial features generated, then converted back to CSC.</p>
<p>If the degree is 2 or 3, the method described in “Leveraging
Sparsity to Speed Up Polynomial Feature Expansions of CSR Matrices
Using K-Simplex Numbers” by Andrew Nystrom and John Hughes is
used, which is much faster than the method used on CSC input. For
this reason, a CSC input will be converted to CSR, and the output
will be converted back to CSC prior to being returned, hence the
preference of CSR.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>XP</strong><span class="classifier">np.ndarray or CSR/CSC sparse matrix, shape [n_samples, NP]</span></dt><dd><p>The matrix of features, where NP is the number of polynomial
features generated from the combination of inputs.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

</dd></dl>

<div class="section" id="examples-using-sklearn-preprocessing-polynomialfeatures">
<h2>Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.preprocessing.PolynomialFeatures</span></code><a class="headerlink" href="#examples-using-sklearn-preprocessing-polynomialfeatures" title="Permalink to this headline">¶</a></h2>
<div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates how to approximate a function with a polynomial of degree n_degree by..."><div class="figure align-default" id="id1">
<img alt="../../_images/sphx_glr_plot_polynomial_interpolation_thumb.png" src="../../_images/sphx_glr_plot_polynomial_interpolation_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/linear_model/plot_polynomial_interpolation.html#sphx-glr-auto-examples-linear-model-plot-polynomial-interpolation-py"><span class="std std-ref">Polynomial interpolation</span></a></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Here a sine function is fit with a polynomial of order 3, for values close to zero."><div class="figure align-default" id="id2">
<img alt="../../_images/sphx_glr_plot_robust_fit_thumb.png" src="../../_images/sphx_glr_plot_robust_fit_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/linear_model/plot_robust_fit.html#sphx-glr-auto-examples-linear-model-plot-robust-fit-py"><span class="std std-ref">Robust linear estimator fitting</span></a></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the problems of underfitting and overfitting and how we can use linea..."><div class="figure align-default" id="id3">
<img alt="../../_images/sphx_glr_plot_underfitting_overfitting_thumb.png" src="../../_images/sphx_glr_plot_underfitting_overfitting_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/model_selection/plot_underfitting_overfitting.html#sphx-glr-auto-examples-model-selection-plot-underfitting-overfitting-py"><span class="std std-ref">Underfitting vs. Overfitting</span></a></span><a class="headerlink" href="#id3" title="Permalink to this image">¶</a></p>
</div>
</div><div class="clearer"></div></div>
</div>


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